Suppose you have a mortgage of $50,000. Expected inflation is 1re, and the nominal interest rate on your mortgage is i. Consider two cases.
i. 1re = 0%; i = 4%
ii. 1re = 10%; i = 14%
a. What is the real interest rate you are paying on your mortgage in each case?
b. Suppose you can deduct nominal mortgage interest pay- ments from your income before paying income tax (as is the case in the United States). Assume that the tax rate is 25%. So, for each dollar you pay in mortgage interest, you pay 25 cents less in taxes, in effect getting a subsidy from the government for your mortgage costs. Compute, in each case, the real interest rate you are paying on your mortgage, taking this subsidy into account.
c. Considering only the deductibility of mortgage inter- est (and not capital-gains taxation), is inflation good for homeowners in the United States?
d. If the central bank is able to keep the inflation rate equal to the target inflation rate every period, will there be dramatic fluctuations in unemployment?
e. Is the central bank likely to be able to hit its inflation target every period?
f. Suppose the natural rate of unemployment, un , changes frequently. How will these changes affect the central bank's ability to hit its inflation target? Explain.